Upload
others
View
9
Download
0
Embed Size (px)
Citation preview
STICKY PRICE INFLATION INDEX: AN ALTERNATIVE CORE INFLATION MEASURE
Ádám Reiff — Judit Várhegyi
Magyar Nemzeti Bank
2012
Abstract
We show that in both time-dependent and state-dependent sticky price models, prices of
sticky price products (i.e. whose price changes rarely) contain more information about
medium term inflation developments than those of flexible price products (i.e. whose price
changes frequently). We do this by establishing a novel measure for the extent of forward-
lookingness of newly set prices, and showing that it is at least 60% when the monthly price
change frequency is less than 15%. This result is robust across various sticky price models.
On the empirical front, we show that the Hungarian sticky price inflation index indeed has a
forward-looking component, as it has favorable inflation forecasting properties on the policy
horizon of 1-2 years to alternative inflation indicators (including core inflation). Both
theoretical and empirical results suggest that the sticky price inflation index is a useful
indicator for inflation targeting central banks.
2/21
Contents
1. Introduction ............................................................................................................................................................... 3
2. Extent of forward-lookingness: theoretical background .................................................................................... 5
2.1. Measurement...................................................................................................................................................... 5
2.2. Results ................................................................................................................................................................. 8
3. Sticky inflation: empirical investigation ............................................................................................................. 10
3.1. Definition of the sticky price index ............................................................................................................. 10
3.2. Time series properties of sticky prices ....................................................................................................... 12
3.3. Forecasting performance ............................................................................................................................... 13
3.3.1. Forecasting performance: framework .................................................................... 14
3.3.2. Forecasting performance: results ......................................................................... 16
3.3.3. Robustness checks ........................................................................................... 17
4. Conclusion ................................................................................................................................................................ 18
3/21
1. INTRODUCTION
The main goal of inflation targeting central banks is to bring medium term inflation rate to a pre-
announced level.1 This medium term objective implies that central bank decision makers should not
respond to short term shocks to inflation which die out in the longer run. However, these temporary cost
shocks – like rising food and oil prices or changing tax rates -, are abundant in the last decade. It is
therefore very important for central banks to separate temporary shocks and high frequency movements
in the inflation processes from the more fundamental (or ―underlying‖) developments. The resulting
underlying inflation indicators should capture medium and long term movements that are not affected by
transitory shocks and are also informative about expected inflation in the relevant policy horizon.
This raises the empirical question of how to define the underlying inflation measure which will guide
central bank decision makers in their attempts to meet the medium term inflation target. The traditional
underlying indicator is core inflation, which excludes the relatively volatile unprocessed food and raw
energy prices from the consumer basket, along with regulated prices that are not informative about the
underlying inflation developments for obvious reasons. But core inflation measures still contain elements
that change with a relatively high frequency (e.g. processed food prices, which might strongly co-move
with the very volatile unprocessed food prices). As an alternative, some central banks use pure statistical
indicators as underlying inflation measures, which try to identify the low frequency elements of the
inflation process by appropriate statistical methods; examples are the (across items) median or trimmed
inflation rates or the volatility-weighted Edgeworth-index of inflation. But there is no consensus in the
literature on which particular inflation measure is the best underlying indicator. For example, Rich and
Steindel (2005) do not find a single underlying inflation measure that performs better relative to other
indicators from all points of view. Similarly for Hungary, Bauer (2011) finds that although some statistical
inflation measures outperform the traditional core inflation indicator, none of them is equally good from
all aspects (smoothness, forecasting ability and small revision).
The goal of this paper is to build a theory-based (i.e. not purely statistical) underlying inflation indicator
for Hungary that outperforms the core inflation measure and is at least as good as the best statistical
indicators. The point of departure is the Atlanta Fed’s sticky price inflation index for the US by Bryan
and Meyer (2010), who argue that prices that change less frequently are more forward-looking and hence
better describe medium term developments in the inflation series; a recent application of the same idea
is for the UK (Millard and O’Grady 2012). The intuition is the following: as gasoline prices change every
week, they are unlikely to contain information about future inflation expectations, as price setters will
be able to account for future changes in the inflation in any week’s price revision. In contrast, restaurant
prices typically change about once a year, say in each January. Therefore when deciding about the price
of meals, restaurant managers know that those newly set prices are likely to stay effective for the entire
1 The reason behind targeting the medium term inflation rate is the time lag with which the economy responds to monetary policy
decisions.
4/21
year. But they also know that they will have to buy materials at spot prices throughout the year, so if
they expect large food inflation for the coming year, they will set higher meal prices for the whole year.
Following this idea, we prepare a sticky price inflation index for Hungary and study its properties in
terms of forecasting the inflation in the relevant policy horizon of 6-8 quarters. Our main contribution is
on the theoretical side: we use prominent sticky price models to justify the intuitive argument of Bryan
and Meyer (2010) that less frequently changing prices have more information content about the longer
run inflation developments. In doing so, we first construct a theory-based measure that describes the
extent of forward-lookingness of newly set prices; and then we show that less frequently changing prices
are indeed more forward looking, and hence contain more information about future developments of
inflation. We also show that this result is robust across models (i.e. state-dependent vs time-dependent
sticky price models) and across model parameterizations.
The intuition of our extent of forward-lookingness measure is that in sticky price models, firms setting a
new price try to make a compromise between two objectives: while they would like to set a price that
maximizes current profits (the ―static optimum‖), they also would like their newly set price to maximize
their expected profits until the next price change (the ―forward-looking optimum‖). The fully optimal
price (or the ―dynamic optimum‖) will be a compromise between these two objectives: it will always be
a weighted average of the static and the forward-looking optima. Our extent of forward-lookingness
indicator then shows how close the fully optimal dynamic price is to the purely forward-looking optimum:
it gives the weight of the purely forward-looking optimum price in the dynamic optimum.2
For the construction of the sticky price inflation index, we use the results of Gábriel and Reiff (2010),
who report product-level price change frequencies for the Hungarian retail sector. Based on store-level
individual price data, they find that the average frequency of price change is 21.5 per cent in Hungary,
but behind this average figure there is substantial product-level heterogeneity. For example, the
frequency of price change in the unprocessed food category is 50.4%, while the same figure for services
in 7.4%. In general, services and traded products’ prices seem to be much stickier than food and energy
prices, which is not surprising given the large international price shocks in the latter two categories. We
use this product-level heterogeneity in price change frequencies to develop our sticky price inflation
index indicator: products whose price changes less frequently than a certain threshold will qualify to the
sticky inflation basket of consumer goods.
We find that the extent of forward-lookingness of newly set prices decreases in the steady-state
frequency of price changes. Quantitatively, the extent of forward-lookingness is at least 60 percent for
price change frequencies below 15 percent per month. This is because less frequently changing prices
are expected to stay effective for a longer time period, so firms must give a higher weight for future
expected profits when deciding about the dynamically optimal price. We show that this result remains
true also in the state-dependent sticky price models, when the timing of the price change is endogenous.
2 Therefore the extent of forward-lookingness indicator has a percentage interpretation.
5/21
With respect to the empirical forecasting ability of the sticky price inflation measure, we find that it
outperforms the traditional core inflation measure both in terms of medium term forecasting ability (in
forecast RMSE) and predicting the direction of future changes in headline inflation. We also find that the
sticky price inflation index is less volatile and more persistent than the traditional underlying inflation
indicators, while flexible price inflation mainly responds to current shocks to inflation.
As discussed, our paper is most closely related to the empirical literature on sticky price measures of
inflation in the US and UK (Bryan and Meyer 2010, Millard and O’Grady 2012). These papers find that
sticky prices contain more information about future inflation and inflation expectations, while flexible
prices are noisy as they mostly respond quickly to changing macroeconomic conditions. These papers,
however, do not provide a formal argument for their intuition of why exactly sticky prices are more
forward-looking. Millard and O’Grady (2012) show that these results are in compliance with a simple
DSGE model using a particular parameterization of a time-dependent Taylor pricing rule; in contrast, we
do this for both time-dependent and state-dependent pricing rules and a lot of alternative
parameterizations. Macallan et al. (2011) also note that sticky prices are important for underlying
inflation: if their inflation remains low, that indicates that firms do not expect accelerating inflation in
the future. Aoki (2001) also highlights the importance of ―core measures‖ modeled in dynamic general
equilibrium framework with nominal price stickiness, and shows that inflation in the sticky sector is a
persistent part of inflation. His conclusion is that sticky inflation is useful for forecasting and an optimal
monetary policy should target sticky price inflation.
The paper is organized as follows. In section 2, we present the theoretical background of sticky prices.
Section 3 presents the empirical investigation: properties of sticky prices, their forecast performance
compared to other underlying inflation measures and robustness checks. Section 4 concludes.
2. EXTENT OF FORWARD-LOOKINGNESS: THEORETICAL BACKGROUND
This section provides theoretical arguments for the claim that sticky prices contain information about
inflation expectations of price setters, and therefore about medium term inflation developments as well.
First we introduce a measure to express the forward-looking content of prices, and then we show
evidence that stickier prices are more forward-looking.
2.1. Measurement
As a starting point, we describe a general sticky price framework in which one can measure the extent of
forward-lookingness. In the baseline sticky price model we have in mind, there is a representative
consumer with a CES consumption aggregator over a continuum of imperfectly substitutable individual
consumption goods, and a continuum of firms, all producing one of the consumption goods with single-
input, constant returns to scale technology. Firms are heterogeneous with respect to their marginal
costs, and they also face some form of price stickiness, but we do not specify the exact form of this. The
sticky price economy of Calvo (1983) and the menu cost economy of Golosov and Lucas (2007) are nested
in this general specification; details can be found in Karádi and Reiff (2012).
6/21
The representative consumer’s CES-aggregator over the different consumption goods (indexed by ) leads
to the familiar constant elasticity of substitution demand curve:
, where is the
representative consumer’s demand for product (produced by firm ), is the consumer’s CES
consumption aggregate, is the nominal price charged by firm , is the aggregate price level
(consistent with the consumption aggregator), and is the elasticity of substitution parameter.
The form of the firms’ single input linear technology is , where is the output of firm , is
the exogenous productivity of firm , and is its labor input, available at perfectly elastic supply at an
exogenously given wage rate . Because of the linear technology, the constant marginal cost of firm is
, so shocks to productivity can also be interpreted as inverse marginal cost shocks for firm . We assume
that log productivity follows an exogenous mean-zero AR(1) process with persistence and
(conditional) standard deviation . Each firm’s objective is to maximize the expected discounted sum of
all future profits, where the per-period profit is given by
, and the firms’ output
are given by the representative consumer’s demand defined above.
We close the model with a simple constant nominal growth assumption: the monetary authority keeps
increasing the money supply – which is equal to nominal output - at a constant rate. As real growth rate
is assumed to be zero, and there is no other source for aggregate uncertainty, the constant nominal
growth rate is equal to the inflation rate, .3
In the absence of any form of price stickiness, firms would set their price in each period to maximize this
per-period profit, leading to the familiar constant mark-up over marginal cost result:
. With
price stickiness, however, the firms’ pricing decision becomes dynamic, and whenever they set a new
price, they have to maximize the sum of their current-period profits and future firm values:
, (1)
where function stands for firm value whenever it changes price, is the firms value,4 and we have
written the firms’ problem in the logs of their relative price ( ) and productivity ( ).5
Equation (1) is the basis of our ―extent of forward-lookingness‖-measure. Its solution is the policy
function of the firm, which we call the dynamically optimal price. Notice that this dynamically optimal
price is a compromise between the static optimum, i.e. the price that maximizes the current-period
profit (the first term in the maximand), and the forward-looking optimum, i.e. the price that maximizes
the future firm value (the second term in the maximand).
3 Under these assumptions, the aggregate wage rate is also constant. For the Calvo-economy, with a linear approximation it can
be expressed analytically, while in the menu cost economy it can be calculated numerically.
4 A similar expression defines the value of the firm whenever it does not change its price, . The firm value itself depends on
these, but the equation that defines it depends on the exact form of price stickiness. In the Calvo-model with exogenously given
price change probability , , while in a state-dependent model, where price changes are endogenous,
.
5 The formal derivation of equation (1) is in Karádi and Reiff (2012).
7/21
Formally, the static optimum is defined as
It depends on the current
productivity (or inverse marginal cost shock) of the firm, which summarizes all the relevant information
for the firm today, but does not contain any expectation for the future. We call this term backward-
looking, emphasizing the fact that this optimum is independent of what the firm expects of the future.
In turn, the forward-looking optimum is defined as . While this optimum
formally only depends on the current productivity (or inverse marginal cost) shocks, through the
expectation operator expected future productivity (or inverse marginal cost) shocks also influence it.
This optimum is therefore inherently forward-looking.
Because of the monotonicity of the profit function around the static optimum, the dynamically optimal
price is always between the static optimum and the forward-looking optimum . As an
illustration, Figure 1 depicts these three types of optima (as a function of the log productivity shock) for
a specific version of the menu cost model.6
Figure 1: Dynamic, static and forward-looking optimum in a menu cost model
Notice that the dynamic optimum is indeed always between the static and the forward-looking optima,
and hence when the two optima coincide for a log productivity shock of about -5 per cent, then it is also
equal to the dynamic optimum. Notice also that the slope of the static optimum is -1, meaning that any
positive (negative) shock to the log productivity decreases (increases) the within-period log optimal price
one-for-one, a direct consequence of the familiar constant mark-up over the marginal cost result.
6 Figure 1 is based on a numerical solution of a menu cost model under a particular parameterization. Changing the
parameterization would not influence the qualitative results.
8/21
Now we can ask the question of how the extent of forward-lookingness could be measured. Intuitively,
the closer the dynamic optimum is to the forward-looking optimum, the larger is the extent of forward-
lookingness. If the dynamic optimum coincided with the forward-looking optimum, the extent of
forward-lookingness would be 100 per cent. On the other hand, if the dynamic optimum coincided with
the static optimum (as in any flexible price model), the extent of forward-lookingness would be 0 per
cent.
Therefore we define the formal measure of the extent of forward-lookingness as the average distance
between the dynamic and static optima, relative to the distance between the forward-looking and static
optima:
. (2)
As the dynamic optimum is always between the static and forward-looking optimum, the ratio in
expression (2) is between 0 and 1 for all possible log productivity shocks ( ). Further, as Figure 1 makes
it clear, there is no reason for this ratio to be independent from log productivity; therefore we take the
weighted average of the ratio, with weights from the steady-state distribution of the firms above their
log productivity levels (denoted by ) in equation (2)).
2.2. Results
We computed the forward-lookingness measure defined in equation (2) for two different sticky price
models (Calvo- and menu cost model) and for many possible parameterizations. Our main focus is on the
relationship between the extent of forward-lookingness and the frequency of price changes.
Figure 2: Frequency of price change and extent of forward-lookingness in the menu cost model
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00
Exte
nt o
f fo
rwar
d-l
oo
kin
gne
ss
Frequency of price change
Frequency of price change and extent of forward-lookingness, MENU COST model, all robustness checks included (on theta, phi, sigma, rho and pi)
9/21
Figure 2 shows the relationship between the frequency of price changes and the extent of forward-
lookingness for a simple model in which the pricing friction is a small price adjustment cost (menu cost).
We obtained this figure by solving the model for different elasticity of substitution parameters ( =3 and
5), menu cost parameters ( ), shock standard deviation parameters ( =0.03, 0.04
and 0.05), shock persistence parameters ( =0, 0.5 and 0.9) and yearly inflation rates ( =0, 0.01, 0.02,
…, 0.12), i.e. for 6,084 different model parameterizations altogether. Note that when the menu cost
parameter was set to 0, that is, when there are no pricing frictions and the frequency of price change
becomes 100 per cent, then the extent of forward-lookingness is always 0 per cent: in this case firms
always change their price, so the dynamic optimum is always the same as the static optimum. On the
other hand, when the menu cost is very large and thus the frequency of price change becomes very
small, then the extent of forward-lookingness is almost 100 per cent: firms know that their current price
will prevail for a long period, and hence they set their price to maximize future profits instead of the
current one. In the intermediate cases, i.e. when the frequency of price change is smaller than 100 per
cent but much larger than 1-2 per cent, there is a negative relationship between the price change
frequency and the extent of forward-lookingness. Irrespective from the specific values of the model
parameters, the extent of forward-lookingness is more than 60 per cent when the frequency is at most
15 per cent, and it is above about 70 per cent when the frequency is not more than 10 per cent.
Figure 3 depicts the same relationship between the frequency of price changes and the extent of
forward-lookingness in the Calvo-model, where in each period a fixed proportion of firms is given the
opportunity to set a new price. Again we have solved the model for different price change frequency
parameters ( =0.025, 0.05, …, 0.5, 0.6, …, 1), shock standard deviation parameters ( =0.12 and 0.15),
shock persistence parameters ( =0, 0.5 and 0.9) and yearly inflation rates ( =0, 0.01, 0.02, …, 0.12),
i.e. for 1,950 different parameterizations of the model. The same result emerges as for the menu cost
model: there is a negative relationship between the price change frequency and the extent of forward-
lookingness; the latter is even higher in this case than in the menu cost model for same price change
frequencies. In the Calvo model with 15 per cent price change frequency, the extent of forward-
lookingness is around 85 per cent, while for a price change frequency of 10 per cent, it mostly exceeds
90 per cent.
10/21
Figure 3: Frequency of price change and extent of forward-lookingness in the Calvo model
3. STICKY INFLATION: EMPIRICAL INVESTIGATION
According to theory, sticky prices contain information about inflation expectations of price setters. In
this section we study the empirical properties of the Hungarian sticky price inflation index. After
defining the index, we investigate both its time-series properties and inflation forecast performance.
3.1. Definition of the sticky price index
Following the approach of sticky price index definitions in other countries,7 we divide the product
category-level consumer price indices into two subcategories: sticky and flexible prices. For this division,
we use the Central Statistical Office’s (CSO) store-level dataset about retail prices on all individual
products in the consumption basket – the basis of the CSO’s monthly inflation calculations. From this
dataset, we calculate the frequency of price changes for about 160 product categories.8 Price indices of
categories with relatively small (large) frequencies belong to the sticky (flexible) CPI. For the
construction of these two aggregate indices, we use the consumption expenditure weights of the CSO.
We make the following transformations of the data before actually weighting the category-level price
indices. First, we get rid of product categories which contain regulated prices. The reason is that these
prices are not determined on the market and hence their information content about expected market
developments is likely to be limited. Second, we correct the price index series with the effects of
7 See Bryan and Meyer (2010) for the US and Macallan et al. (2011) for the UK.
8 In principle, we could use item-level frequencies as well, calculated for about 900 individual products. We do not do this as we
only have official price indices for the 160 product categories. Most probably, this does not influence the results: products within
the product categories are similar and in most cases their frequency of price change is similar. For example, in the ―Pork‖ category
the category-level frequency is 0.427, while the product-level frequencies are 0.420, 0.450, 0.454 and 0.413 (for short loin, pork
ribs, pork leg and pork flitch, respectively).
0,0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1,0
0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 0,80 0,85 0,90 0,95 1,00
Exte
nt o
f fo
rwar
d-l
oo
kin
gne
ss
Frequency of price change
Frequency of price change and extent of forward-lookingness, CALVO model, robustness checks included (eps, sigma, rho and pi)
11/21
indirect tax changes (e. g. Value-Added Tax (VAT)). The VAT-changes in our sample were large (out of
the six VAT-change episodes, three were as large as five percentage points), with large inflation effects
in the monthly inflation series, so these episodes are huge outliers. Third, we seasonally adjusted the
monthly inflation series. We do this adjustment at the sticky/flexible CPI level (i.e. on the weighted sum
of indices), instead of doing it separately on each category-level price index, as this provides smoother
seasonally adjusted series. Fourth, for the frequency calculations, we used posted prices as opposed to
sales-filtered or regular prices. We did not filter out sales as they might be correlated with inflation
developments.
Obviously, we need a threshold frequency value below which items belong to the sticky part of the CPI.
The choice of this is arbitrary. Two natural candidates are the weighted median and the weighted mean
frequencies. Based on the numerical results of Section 2, we consider a third, theoretical threshold of 15
per cent: for this – according to our measure –, the extent of forward-lookingness is always more than 60
per cent. Table 1 shows the three threshold candidates. The weighted median is in fact close to the
theoretical threshold (17 percent vs 15 percent), hence the implied mean price duration is circa 6-7
month for both. For the weighted mean frequency, the implied mean duration between two price
changes is somewhat shorter, less than 5 month.
For our baseline specification, we decided to use the theoretical threshold of 15 percent for two reasons.
First, for this threshold about 40 per cent of the consumption basket (excluding regulated prices) is in
the sticky CPI index, so both the sticky and flexible CPIs are based on a relatively large number of
product categories.9 Second, the difference between the theoretical threshold and the weighted median
threshold are product categories whose frequency is between 15 and 17 percent. These are mostly
processed food items that are sensitive to the relatively volatile food price shocks; we preferred to
allocate these items into the flexible CPI sub-index. Note that we performed robustness checks for the
sensitivity of our results for the sticky-flexible threshold selection (see subsection 3.3), and found that
this particular threshold value does not influence our results qualitatively.
Table 1: The different threshold values
Note: The last column shows the relative CPI weights of sticky prices, after excluding regulated prices.
Categories that we include into the sticky price sub-index are listed in Table 2. Most market services and
industrial products belong to the sticky CPI sub-index. In turn, the flexible-price inflation index contains
almost all food items, fuel, alcohol and tobacco, i.e. product categories that are subject to larger
external shocks for obvious reasons. The total consumption weight of the sticky CPI index is 32.6
9 This implies that individual product categories cannot have a big impact on either of the sub-indices.
Frequency
(per cent)
Price change
(month)
Weight of
sticky prices
median 17 6.0 43.8
average 21 4.8 58.5
theory 15 6.7 40.4
12/21
percent, and almost all of this belongs to the core inflation.10 Thus the sticky CPI index can be
interpreted as a ―super‖ core inflation measure, which contains the sticky components of the official
core inflation measure.
Table 2: List of products in the sticky price index
3.2. Time series properties of sticky prices
Figure 4 depicts the Hungarian sticky and flexible inflation series – as defined above - between January
2002 and 2011 December, together with the headline CPI series (excluding regulated prices and indirect
tax changes). It is apparent from the figure that sticky-price inflation is much less volatile than flexible-
price inflation. This observation is consistent with our theoretical argument that flexible prices tend to
react to current shocks, while sticky prices reflect changes in expectations – which are much smoother -
to a larger extent.11
In order to further investigate the empirical reasonability of this argument, we have also calculated the
variance and the first-order autocorrelation (or persistence) of the different inflation series. We also
capitalized on the large disinflation episode between 1998 and 2002, when headline annual inflation
rates decreased from double-digit to 4-5 per cent, by comparing volatility measures including and
excluding this disinflation period. Table 3 contains the results.
In terms of volatility, there is indeed a reduction between 2002 and 2011 (relative to the 1998-2011
one). For the headline CPI, this reduction is about 35 per cent (from 18.5 to 11.5). Interestingly, this
10 Besides the headline CPI, the CSO also publishes a core inflation measure. 67% of the consumption basket belongs to the core
inflation items. In essence, it excludes the unprocessed food, energy and regulated prices from CPI, so it is widely used as an
underlying indicator to measure the inflation pressure.
11 Of course, this is not the only possible explanation for the less volatile sticky inflation series.
Description Frequency Description Frequency Description Frequency
Theatres 0.024 Cable television subscription 0.064 Infant's clothing 0.091
Health services 0.031 Meals at canteens by subscription 0.065 Household repairing and maintenance goods0.092
Repairs of recreational goods 0.035 Men's underwear 0.067 Recording media 0.094
Photographic services 0.035 Buffet products 0.069 Radio sets 0.100
Cinemas 0.038 Kitchen and other furniture 0.069 Pets foods 0.101
Repairs of major household appliances 0.039 Furnishing fabrics, carpets, curtains 0.069 Confectionery and ice-cream 0.103
Taxi 0.041 Houshold paper and other products 0.072 Cooking utensils, cutlery 0.105
Cup of coffee in catering 0.043 Children's footwear 0.075 Jewellery 0.106
Transport of goods 0.044 Bed and table linen 0.075 Heating and cooking appliances 0.112
Repairs, maintenance of vehicles 0.046 Women's underwear 0.076 Vacuum cleaners, air-conditioning 0.112
Rent without local government 0.046 Living, dining- room furniture 0.078 Men's footwear 0.122
Meals at restaurants not by subscription 0.049 Parts and accessories of "do it-yourself" 0.079 Recreation abroad 0.122
Cleaning, washing 0.050 Sport and camping articles, toys 0.080 Clothing accessories 0.131
Repairs and maintenance of dwellings 0.051 Educational services 0.081 Videos, tape recorders 0.135
Clothing materials 0.052 Passenger cars, new 0.085 Beef 0.136
Personal care services 0.052 Passenger cars, second-hand 0.085 Other meat 0.136
Repairs clothing and footwear etc. 0.053 Motorcycle 0.085 Briquettes, coke 0.136
Other, not administered services 0.053 Bicycle 0.085 Dried vegetables 0.139
Haberdashery 0.055 Computer, cameras, phone etc. 0.087 Firewood 0.140
Leather goods 0.055 Newspapers, periodicals 0.088 Wine 0.142
Tyres, parts and accessories for vehicles 0.064 Books 0.088 Edible offals 0.146
Maintenance cost at private houses 0.064 School and stationery supplies 0.090 Candies, honey 0.146
13/21
reduction seems to come almost entirely from the reduction in the volatility of sticky price inflation:
there the reduction is from 10.2 to 3.2. In turn, the volatility of the flexible inflation series did not
change significantly (43.7 vs 37.0). This is fully consistent with our view that flexible prices react to
exogenous shocks (for which there is no reason to believe to have declined from 2002), while sticky
prices contain more information about expectations, which might have been anchored once the headline
inflation rate was moderated.
Figure 4: Sticky versus flexible inflation (annualized monthly changes)
In terms of persistence, sticky inflation seems to be much more persistent than its flexible inflation
counterpart. Given the absence of the large shocks in the sticky inflation series, this is hardly surprising.
Table 3: Variance of sticky and flexible prices
Note: Variance is calculated from annualized monthly changes.
3.3. Forecasting performance
In this sub-section we investigate whether the sticky inflation series contains more information about
future headline inflation rates – which it should if it indeed contains an expectation component. We do
this by studying the relative forecast performance of various inflation measures (including the sticky
CPI), by comparing (1) their effect on the Root Mean Squared Errors (RMSEs) of out-of-sample forecasts
and (2) their ability to predict future changes in headline inflation. First we describe the methodology in
details, and then we turn to the results.
-15
-10
-5
0
5
10
15
20
Jan-0
2
Jul-
02
Jan-0
3
Jul-
03
Jan-0
4
Jul-
04
Jan-0
5
Jul-
05
Jan-0
6
Jul-
06
Jan-0
7
Jul-
07
Jan-0
8
Jul-
08
Jan-0
9
Jul-
09
Jan-1
0
Jul-
10
Jan-1
1
Jul-
11
(%)
annualise
d m
onth
ly c
hange
CPI flexible sticky
sample sticky flexible CPI
1998-2011 10.2 43.7 18.5
2002-2011 3.2 37.0 11.5
AR coefficient 1998-2011 0.86 0.43 0.55
Variance
14/21
3.3.1. Forecasting performance: framework
We evaluate the forecasting performance of the sticky and flexible CPI indices in two ways. First, we
study how the inclusion of various inflation measures changes the RMSE of out-of-sample forecasts of
headline inflation, relative to a benchmark model. Second, we check whether the difference between
the sticky and headline CPIs is a significant predictor of future changes in the headline inflation rate.
More precisely, for the evaluation of the out-of-sample forecasting performance, we estimate the
following regression:
(3)
where denotes the monthly change of headline CPI (excluding regulated prices), st is the monthly
change of the explanatory variable (sticky or flexible CPI, core inflation, or other inflation measure, also
excluding regulated prices), B(L) is the lag operator, is the error term, and h is the forecast horizon.
We do the forecasting exercise for each explanatory variable separately, and in a recursive manner.
First, we estimate equation (3) on data between 1998 and 2007. Based on the estimated parameters, we
forecast the h-period ahead (cumulative) inflation rate, and compare it to its actual value. Then we add
one observation and repeat the procedure: estimate model parameters, forecast the inflation rate, and
compare with its actual value. Then we repeat this procedure until we forecast the cumulative inflation
rate ending in December 2011. Finally, we calculate the RMSE from the forecast errors to have an RMSE
figure for each candidate explanatory variable.
Our benchmark model is a simple autoregressive model (that is, when . In the alternative models,
we replace the CPI inflation variable with either the sticky or flexible CPI, or with one of the underlying
inflation indicators of Bauer (2011): the Edgeworth-weighted inflation index or the demand-sensitive
inflation measure.12 Figure 5 depicts these alternative inflation measures, while Table 4 provides their
correlation matrix; both indicate strong co-movements. To evaluate their relative forecast performance,
we always calculate relative RMSE-s, which are relative to the benchmark autoregressive model. A
relative RMSE of less than 100 per cent indicates better forecasting performance than that of the
benchmark model.
12 Bauer (2011) concluded that among the several underlying inflation indicators he investigated, the Edgeworth-weighted index
had the best properties in terms of smoothness, robustness to revisions and forecasting performance. This index is an inverse-
volatility weighted index of category-level price indices. Demand-sensitive inflation index is the core inflation index excluding the
processed food items.
15/21
Figure 5: Different underlying inflation indicators (yearly changes)
Table 4: Correlation matrix of different underlying indicators
Note: Based on monthly changes.
We investigate the forecasting performance of the different inflation indicators on five different
horizons: 1, 3, 6, 12 and 24 months. If our theoretical argument about the expectation content of the
sticky inflation measure is correct, then we should see a better forecasting performance of that indicator
especially on the longer horizons.
For the recursive estimation, we always use real-time data, i.e. data that were available at the moment
of forecasting. This means that we seasonally adjust the time series at each possible forecasting date,
rather than simply using the seasonally adjusted series as of December 2011. This might be important
because of uncertainty in the seasonal adjustment procedure or data revisions.13
Besides this RMSE-comparison, we also assess the forward-lookingness of the sticky price CPI in a more
direct way. The idea is that if our theoretical argument about the expectation content of sticky prices is
correct, then the actual gap between the sticky price index and the headline CPI can be informative
about the future developments of the headline CPI. Following Cogley (2002), Amstad and Potter (2009)
and Bauer (2011), we estimate the following equation:
13 For the Edgeworth-weighted index, we do not have real-time data, so we do the calculations with the 2011 December version of
the data. In the robustness section, however, we show that working with real time data – when available - actually does not change
our qualitative results.
0
1
2
3
4
5
6
0
1
2
3
4
5
6
Jan-0
4M
ar-
04
May-0
4Jul-
04
Sep-0
4N
ov-0
4Jan-0
5M
ar-
05
May-0
5Jul-
05
Sep-0
5N
ov-0
5Jan-0
6M
ar-
06
May-0
6Jul-
06
Sep-0
6N
ov-0
6Jan-0
7M
ar-
07
May-0
7Jul-
07
Sep-0
7N
ov-0
7Jan-0
8M
ar-
08
May-0
8Jul-
08
Sep-0
8N
ov-0
8Jan-0
9M
ar-
09
May-0
9Jul-
09
Sep-0
9N
ov-0
9Jan-1
0M
ar-
10
May-1
0Jul-
10
Sep-1
0N
ov-1
0Jan-1
1M
ar-
11
May-1
1Jul-
11
Sep-1
1N
ov-1
1
%%
Range of underlying inflation indicatorsCore inflation excluding indirect tax changes"Demand sensitive" inflationSticky prices
sticky edgew demand sensitive core
sticky 1.000 0.909 0.905 0.874
edgew 0.909 1.000 0.904 0.938
demand sensitive 0.905 0.904 1.000 0.880
core 0.874 0.938 0.880 1.000
16/21
(4)
where and are the yearly changes in the headline and the sticky CPI indices, respectively. The
interpretation is quite straightforward. Parameter tells us whether and how the evolution of the
headline CPI (over a time horizon of h months) is connected to current differences between the sticky
and headline CPI. If, for example, we find and , then the current deviation perfectly explains
the future inflation developments. If is less than unity, but significant then the deviation predicts the
direction of the change in the headline CPI correctly, but understates its effect. If is greater than
unity, then the deviation overstates the effect. Equation (4) with core inflation as the explanatory
variable serves as a benchmark model, and in this case we again do the estimation on real-time data.
3.3.2. Forecasting performance: results
The left panel of Table 5 reports the relative (to the core inflation) RMSEs of the alternative inflation
indicators estimating equation 3. Overall, we find that the sticky-price-based inflation forecasts are
more accurate relative to the benchmark autoregressive model. In short run (on 1-3 months horizons),
the improvement is not significant and the core inflation-based model’s forecast performance is close to
the sticky price-based model. But the relative accuracy increases on longer forecast horizons. In 1 year
horizon, sticky prices tend to be more accurate, in line with property that many sticky prices change only
once in every 12 month. So because of this forward-lookingness, sticky price measures can serve as a
proxy for inflation expectations. In contrast, flexible prices are noisy and do not improve the RMSE. As
the forecast horizons get longer, the accuracy of flexible prices is worsening, relative to the benchmark
autoregressive model. The relative RMSEs of the demand sensitive inflation and Edgeworth-index show
pretty good forecast performance compared to benchmark autoregressive model.
Table 5: Relative performance of measures based on real time data
Note: EW based on last vintage sample.
Table 6 shows the estimated parameter from equation 4. The estimated α parameters do not differ
significantly from zero, so we do not report them. The results strengthen our claim about the forward-
lookingness properties of sticky prices: the actual difference between the year-on-year sticky price index
and headline inflation helps predicting the future headline inflation. The Edgeworth- and demand
sensitive inflation indices have similar attractive predictive power. At the same time, the flexible prices
are noisy and do not predict the direction of future changes in inflation. The estimated parameters of
flexible prices are zero also in long run. So flexible prices are mainly determined by one-off shocks, and
horizon
(month)sticky flex
demand
sensitiveEW core
1 106% 107% 103% 96% 104%
3 96% 108% 97% 90% 103%
6 88% 111% 89% 92% 98%
12 85% 122% 84% 88% 101%
24 66% 119% 68% 81% 97%
17/21
these shocks do not affect medium and long run inflation. As in the former empirical framework, the
demand sensitive inflation and Edgeworth-index shows a similar result as the sticky-price inflation index.
So these alternative indicators can also give indication about future inflation changes.
Table 6: Estimated parameter in forward-lookingness based on real time data
3.3.3. Robustness checks
We performed several robustness checks for our results. First, we replaced real-time data with data as of
December 2011 to evaluate the magnitude of the differences stemming from data and seasonal
adjustment revisions. (This exercise is important for the evaluation of the previous results on the
Edgeworth-weighted index, as we do not have real-time data for it.) Second, we changed the in-sample
data period from 1998-2007 to 2002-2007, i.e. dropped the 1998-2001 period of heavy disinflation, which
might have had a big impact on our results. Third, we estimated alternative specification for equation 3
and 4. Finally, we changed the threshold value that we use to separate the consumer basket into sticky
and flexible prices.
The main results are the followings:
1. Tables 7 and 8 in the Appendix show that our results are quite similar when calculated on the
last (December 2011) vintage of the data. The message is that revisions in the seasonally
adjusted series are not significant. Comparing Tables 5 and 6 implies that under seasonal
adjustment revisions, the sticky CPI gets slightly worse in terms of the relative RMSE-s and
slightly better in terms of forward-lookingness, but the changes are quantitatively small and our
qualitative results are unchanged.
2. When we calculated on shorter sample, the results slightly changed for equation (3) (see Table 9
in the Appendix). The relative performance of sticky price index is quite similar to benchmark
autoregressive model. But the sticky price index is still not worse than the other alternative
underlying indices (demand-sensitive and Edgeworth-indices). The main reason of this change is
that Hungary did not have a strong disinflation period after 2002, so the volatility of the
explanatory variables is much smaller and hence the parameter estimates are less reliable. In
contrast, Table 10 of Appendix shows that the estimated parameters were robust to alternative
sample period in case of equation (4), so the sticky price index preserves its attractive predictive
properties.
horizon
(month)sticky flex
demand
sensitiveEW core
1 0.03 0.02 0.04 0.09 0.06
3 0.18 0.04 0.14 0.32 0.14
6 0.29 0.03 0.21 0.49 0.17
12 0.37 0.00 0.32 0.54 0.05
24 0.59 -0.05 0.56 0.71 0.13
18/21
3. We estimated the equation (3) in alternative specification as well: we included the lagged value
of the headline CPI as an additional explanatory variable. As the headline CPI is a persistent
process, the estimated parameters of this variable were highly significant. But despite the better
fit of the forecast equation, the relative forecast errors did not improve notably (Table 11 in the
Appendix). In case of equation (4), we also performed the estimation with annualized monthly
changes of CPI (the baseline specification was yearly inflation). The estimated parameters
improved significantly and do not differ from unity in long run (Table 12 in the Appendix).
4. In the baseline case, the threshold frequency is 15 per cent. We repeated the estimations with
two alternative threshold values: 10 and 20 per cent. According to Tables 13 and 14 in the
Appendix, the qualitative results did not change. It is apparent from Table 13 that the stricter is
the sticky price threshold, the more forward-looking the sticky price index becomes, which is an
intuitive result. According to Table 14, different threshold values do not change the results of
estimating equation (4) significantly.
4. CONCLUSION
In this paper we construct a theory-based alternative underlying inflation measure, the sticky price
inflation index. Intuitively, it can give indication about future price changes. We have shown in a general
model of sticky prices why sticky prices are more forward-looking. To do so, first we have defined a
formal measure of the extent of forward-lookingness, and then we have shown that in both time-
dependent and state-dependent sticky price models, there is negative connection between the frequency
of price change and extent of forward-lookingness, meaning that stickier prices are more forward-
looking. Quantitatively, we found that when the monthly frequency of price changes is at most 15 per
cent, the extent of forward-lookingness is at least 60 per cent.
Using the theoretical threshold value for the frequency of price change of 15 per cent, we divided the
consumer price index into sticky and flexible price indices. Our empirical investigation proved that sticky
prices have smoother time series than flexible prices and their reaction to one-off price shock is limited.
The empirical investigations underpinned their better forecast performance, so at longer horizon sticky
prices tend to be more accurate than flexible prices. Also, sticky price measures can serve as a proxy for
inflation expectations.
The comparison to alternative underlying inflation measures showed that the forecast performance of
the sticky price index is similar to the best atheoretical underlying prices indices (Edgeworth-index and
demand sensitive inflation). A clear advantage of the sticky price index is that it is more founded by
theory. Another attractive feature is that the sticky price index is calculated from a fixed consumer
basket, while the alternative statistical indices filter the most volatile items from the whole CPI basket
(e.g. trimmed mean) or change their weight system (e.g. Edgeworth index) month by month, so their
revision can be significant. In contrast, the only source of revision in the sticky price index is one
stemming from seasonal adjustment.
19/21
References
AOKI, K. (2001): ―Optimal Monetary Policy Responses to Relative-Price Changes‖, Journal of Monetary
Economics, Vol. 48.
AMSTAD, M. and POTTER, S. (2009): ―Real Time Underlying Inflation Gauges for Monetary Policymakers‖,
Federal Reserve Bank of New York, Staff Reports, No. 420.
BAUER, P. (2011): ―Underlying inflation measures (Inflációs trendmutatók, available only in Hungarian)‖,
MNB Operating Papers 91, February 2011.
BILS, M. and KLENOW, P. J. (2004): ―Some Evidence on the Importance of Sticky Prices‖, Journal of
Political Economy, Vol. 112 No. 5.
BRYAN, M. F. and MEYER, B. (2010): ―Are Some Prices in the CPI More Forward Looking Than Others? We
Think So‖, Economic Commentary, Federal Reserve Bank of Cleveland, No. 2010-2.
CALVO, G. A. (1983): ―Staggered Prices in a Utility-Maximizing Framework‖, Journal of Monetary
Economics, Vol. 12, No. 3.
COGLEY, T. (2002): ―A Simple Adaptive Measure of Core Inflation‖, Journal of Money, Credit and
Banking, Vol. 34, No. 1.
GÁBRIEL, P. and REIFF, Á. (2010): ―Price Setting in Hungary – A Store-Level Analysis‖, Managerial and
Decision Economics 31, No. 2-3.
GOLOSOV, M. and LUCAS Jr., R. E. (2007): ―Menu Costs and Phillips Curves‖, Journal of Political
Economy, University of Chicago Press, vol. 115.
KARÁDI, P. and REIFF, Á. (2012): ―Large Shocks in Menu Cost Models‖, ECB Working Paper 1453, July
2012.
MACALLAN, C., TAYLOR, T. and O’GRADY, T. (2011): ―Assessing the Risk to Inflation from Inflation
Expectations‖, Bank of England, Quarterly Bulletin, 2011Q2.
MILLARD, S. and O’GRADY, T. (2012): ―What Do Sticky and Flexible Prices Tell Us?‖ Bank of England,
Working Paper No. 457.
RICH, R. and CH. STEINDEL (2005) ―A Review of Core Inflation and an Evaluation of its Measures‖, Federal
Reserve Bank of New York, Staff Reports, No. 236.
RICH, R. and CH. STEINDEL (2007) ―A Comparison of Measures of Core Inflation‖, Federal Reserve Bank of
New York, Economic Policy Review.
20/21
Appendix: Additional Tables for Robustness Checks
Table 7: Relative performance of measures on last vintage
Table 8: Estimated parameter in forward-lookingness on last vintage
Table 9: Relative RMSE in different sample period
Note: Based on real time data.
Table 10: Estimated parameter in different sample period
horizon
(month)sticky flex
demand
sensitiveEW core
1 99% 115% 99% 96% 102%
3 91% 116% 94% 90% 100%
6 88% 123% 93% 92% 101%
12 80% 131% 86% 88% 100%
24 64% 127% 70% 81% 98%
horizon
(month)sticky flex
demand
sensitiveEW core
1 0.04 0.02 0.05 0.09 0.08
3 0.19 0.03 0.15 0.32 0.19
6 0.33 0.04 0.26 0.49 0.26
12 0.40 0.03 0.39 0.54 0.12
24 0.62 -0.01 0.66 0.71 0.21
horizon
(month)sticky flex
demand
sensitiveEW core
1 109% 102% 105% 96% 103%
3 105% 102% 106% 93% 106%
6 103% 102% 103% 95% 103%
12 100% 100% 96% 90% 94%
24 134% 93% 118% 96% 90%
horizon
(month)sticky flex
demand
sensitiveEW core
1 0.01 0.02 0.03 0.06 0.04
3 0.10 0.03 0.07 0.26 0.09
6 0.19 0.02 0.14 0.38 0.13
12 0.22 -0.02 0.22 0.31 -0.04
24 0.38 -0.03 0.42 0.50 -0.02
21/21
Table 11: Relative RMSE in alternative specification
Table 12: Estimated parameter in alternative specification
Table 13: Relative RMSE at different threshold value
Table 14: Estimated parameter at different threshold value
horizon
(month)sticky flex
demand
sensitiveEW core
1 98% 101% 97% 93% 99%
3 92% 101% 94% 90% 100%
6 90% 107% 90% 93% 98%
12 84% 114% 82% 87% 97%
24 65% 104% 67% 81% 93%
horizon
(month)sticky flex
demand
sensitiveEW core
1 0.49 -0.26 0.58 0.62 0.55
3 0.75 -0.45 0.86 0.92 0.74
6 0.98 -0.60 1.11 1.23 1.05
12 0.85 -0.64 1.02 1.02 0.93
24 0.89 -0.86 1.08 1.06 0.94
horizon
(month) sticky10 sticky15 sticky20 flex10 flex15 flex20
1 105% 106% 101% 106% 107% 111%
3 96% 96% 94% 107% 108% 114%
6 83% 88% 87% 110% 111% 118%
12 83% 85% 89% 119% 122% 133%
24 60% 66% 74% 117% 119% 125%
horizon
(month) sticky10 sticky15 sticky20 flex10 flex15 flex20
1 0.03 0.03 0.04 0.03 0.02 0.01
3 0.13 0.18 0.17 0.04 0.04 0.02
6 0.23 0.29 0.25 0.04 0.03 0.01
12 0.25 0.37 0.31 0.00 0.00 0.00
24 0.49 0.59 0.43 -0.04 -0.05 -0.02